All naturally occurring metals have negative permittivity up to the plasma frequency vp, but the zero permittivity frequency is frequently accompanied by large losses. These plasma frequencies are often in the ultraviolet or visible range and are many orders of magnitude higher than microwave frequencies. In doped semiconductors, vp can be moved from higher frequencies to the far infrared. For the purpose of constructing metamaterials with metallic structures, it is desirable to adjust the plasma frequency to a reasonable value to improve the impedance matching and transmission. The experimental and theoretical demonstration of low plasma frequencies resulting from an array of thin metal wires as originally conceived by Pendry, and later in Ref. 2, was a major stimulus for metamaterials research. An array of thin metal wires lowers the plasma frequency because of the diluted effective electron density and effective mass. The effective electron density is obtained by the ratio of volume occupied by the metallic thin wire to the vacuum space, and the effect of the self-inductance of the structure can be considered as a contribution to the effective mass of the electrons. Therefore, if the effective electron density neff decreases, and the effective mass meff increases, then the plasma frequency vp decreases. In other words, the plasma frequency of a 2D array of metal thin wires depends on the geometrical parameters, the period p, and the diameter d of the metal wire.
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